Question

Giải phương trình

a) \(\sqrt[3]{2x+3}-\sqrt[3]{x+4}+x+4=0\)

b) \(\sqrt[3]{x^2+3x+1}+x^2=\sqrt[3]{5x+1}+2x\)

Answer 1

Câu a đề sai

Câu b:

Đặt \(\left\{{}\begin{matrix}\sqrt[3]{x^2+3x+1}=a\\\sqrt[3]{5x+1}=b\end{matrix}\right.\) \(\Rightarrow a^3-b^3=x^2-2x\)

Pt trở thành:

\(a-b+a^3-b^3=0\)

\(\Leftrightarrow a-b+\left(a-b\right)\left(a^2+ab+b^2\right)=0\)

\(\Leftrightarrow\left(a-b\right)\left(a^2+ab+b^2+1\right)=0\)

\(\Leftrightarrow a=b\)

\(\Leftrightarrow x^2+3x+1=5x+1\)

\(\Leftrightarrow...\)